- In this question you must show all stages of your working.
\section*{Solutions based entirely on calculator technology are not acceptable.}
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\caption{Figure 2}
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A brick is in the shape of a cuboid with width \(x \mathrm {~cm}\) ,length \(3 x \mathrm {~cm}\) and height \(h \mathrm {~cm}\) ,as shown in Figure 2.
The volume of the brick is \(972 \mathrm {~cm} ^ { 3 }\)
- Show that the surface area of the brick,\(S \mathrm {~cm} ^ { 2 }\) ,is given by
$$S = 6 x ^ { 2 } + \frac { 2592 } { x }$$
- Find \(\frac { \mathrm { d } S } { \mathrm {~d} x }\)
- Hence find the value of \(x\) for which \(S\) is stationary.
- Find \(\frac { \mathrm { d } ^ { 2 } S } { \mathrm {~d} x ^ { 2 } }\) and hence show that the value of \(x\) found in part(c)gives the minimum value of \(S\) .
- Hence find the minimum surface area of the brick.